- #1

- 3

- 0

The first problem:

## Homework Statement

A slender rod with length L has a mass per unit length that varies with distance from the left-hand end, where x=0, according to dm/dx=gamma*x, where gamma has units of kg/m^2.

Calculate the total mass of the rod in terms of gamma and L.

Use I=int r^2dm to calculate the moment of inertia of the rod for an axis at the left-hand end, perpendicular to the rod. Use the expression you derived in part (a) to express I in terms of M and L.

Repeat part (b) for an axis at the right-hand end of the rod.

## Homework Equations

I=int r^2dm

and dm/dx=gamma*x

## The Attempt at a Solution

I got the first part by integrating dm/dx; the answer was (gamma*L^2)/2

I'm not sure how to do the second part. I originally solved for dm and plugged that into the integral and solved, but the program said gamma was not part of the answer. Is that correct?

The second problem:

## Homework Statement

Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass M and radius R about an axis perpendicular to the hoop's plane at an edge.

## The Attempt at a Solution

I'm not sure where to start on this one. My first issue is I'm not sure where the axis is, and once I figure out that, I'm not sure what to do.

Thanks for any help!